RUBIES: The Evolution of the Ionization Parameter from 0 < z < 9

The dimensionless ionization parameter, U=q/c, where q is the ratio of the local ionizing photon flux to the local hydrogen density, is a key metric to parameterize nebular conditions. Prior to JWST, the rest-frame optical emission lines and their ratios which trace the ionization parameter (e.g., O32=[OIII]/[OII]) were inaccessible at high redshifts. Here we quantify, for the first time, the evolution of the ionization parameter in galaxies across the last 13 billion years of cosmic time by comparing JWST/NIRSpec PRISM and G395M spectroscopy of 434 galaxies at 3<z<9 from the RUBIES survey with z<3 samples from SDSS, LEGA-C, and KBSS. We leverage a large suite of photoionization models to infer U from [OIII] and [OII]. We find that U increases with redshift and specific star formation rate (sSFR), and decreases with stellar mass. Crucially, and in contrast to previous linear best-fit calibrations, our inference results in a systematic uncertainty in logU of ~0.3 dex at zero measurement uncertainty due to the wide range of models that predict the same O32 ratio without informative priors. We compare to SPHINX20 and LUMEN simulations and find that the simulated galaxies exhibit higher O32 ratios at fixed redshift and stellar mass compared to RUBIES observations. Finally, we combine the predictive power of observed and inferred quantities with multivariate relations to estimate U from redshift, stellar mass, and sSFR for use where O32 is not available. We find that U increases at fixed stellar mass and sSFR by a factor of ~4 from z=2 to z=6, demonstrating that the redshift evolution encapsulates physics beyond that traced by stellar mass and sSFR alone. Finally, we show that a toy model with the first order assumption that HII region volume is proportional to galaxy volume can explain the excess redshift dependence of logU as being consistent with observed evolution in galaxy sizes.